Thank you for very quick reply, Paul. I mean if the cell size is 1/2 cutoff, then an atom in a central bin may neglect some neighbors in a bin far away.
For instance, atom i is in the middle of cell 0 may not check the atom j in cell 2 (because cell 2 is not adjacent to 0) even though the distance between them is smaller than cutoff (because the size of cell 1 is only 1/2 cutoff).
The skin parameter is only applied for atoms in the neighboring cells of cell 0 and then is not applicable to atom j in this case.
An illustration is attached for what I mean.